For a time-dependent wavefunction \(|\psi (t)\rangle \)  and in the Schrödinger picture, the instantaneous QFI density associated with a local spin operator is defined as  [1]}, [2]}, [3]}
\(f_\mathrm {Q}(q, t) &=& \frac{4}{N} \sum _{ij}e^{iq(r_i-r_j)}\left[ \left\langle \psi (t)\left| {S}_i^z{S}_j^z\right|\psi (t)\right\rangle \right.\nonumber \\&&\left.- \left\langle \psi (t)\left|{S}_i^z\right|\psi (t)\right\rangle \left\langle \psi (t)\left|{S}_j^z\right|\psi (t)\right\rangle \, \right]\,.\) 
